JEE Mains · Physics · STD 11 - Newtons laws of motion
- JEE Mains 2016
- Hard
- MCQ
A particle of mass \(m\) is acted upon by a force \(F\) given by the empirical law \(F = \frac{R}{{{t^2}}}\,v(t)\). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(log\, v(t)\) against \(\frac{1}{t}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}
From\,F = \frac{R}{{{t^2}}}v\left( t \right) \Rightarrow m\frac{{dv}}{{dt}} = \frac{R}{{{t^2}}}v\left( t \right)\\
Integrating\,both\,sides\,\int {\frac{{dv}}{v} = \int {\frac{{Rdt}}{{m{t^2}}}} } \\
In\,v = - \frac{R}{{mt}}\\
\therefore \,In\,v\, \propto \frac{1}{t}
\end{array}\)
From\,F = \frac{R}{{{t^2}}}v\left( t \right) \Rightarrow m\frac{{dv}}{{dt}} = \frac{R}{{{t^2}}}v\left( t \right)\\
Integrating\,both\,sides\,\int {\frac{{dv}}{v} = \int {\frac{{Rdt}}{{m{t^2}}}} } \\
In\,v = - \frac{R}{{mt}}\\
\therefore \,In\,v\, \propto \frac{1}{t}
\end{array}\)
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